Solution to a System of Equations
The set of all values that can be substituted for the variables in each equation of a system and that satisfy all the equations of the system simultaneously.
Example
Consider the system of equations y = 2x and y = 4x² − 1 :
The solutions to this system are the ordered pairs of coordinates ([latex]\frac{1 + \sqrt{5}}{4}[/latex],[latex]\frac{1 + \sqrt{5}}{2}[/latex]) and ([latex]\frac{1 – \sqrt{5}}{4}[/latex],[latex]\frac{1 – \sqrt{5}}{2}[/latex]).